Detect if an element is visible with jQuery

if($('#testElement').is(':visible')){
    //what you want to do when is visible
}

You're looking for:

.is(':visible')

Although you should probably change your selector to use jQuery considering you're using it in other places anyway:

if($('#testElement').is(':visible')) {
    // Code
}

It is important to note that if any one of a target element's parent elements are hidden, then .is(':visible') on the child will return false (which makes sense).

jQuery 3

:visible has had a reputation for being quite a slow selector as it has to traverse up the DOM tree inspecting a bunch of elements. There's good news for jQuery 3, however, as this post explains (Ctrl + F for :visible):

Thanks to some detective work by Paul Irish at Google, we identified some cases where we could skip a bunch of extra work when custom selectors like :visible are used many times in the same document. That particular case is up to 17 times faster now!

Keep in mind that even with this improvement, selectors like :visible and :hidden can be expensive because they depend on the browser to determine whether elements are actually displaying on the page. That may require, in the worst case, a complete recalculation of CSS styles and page layout! While we don’t discourage their use in most cases, we recommend testing your pages to determine if these selectors are causing performance issues.

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Expanding even further to your specific use case, there is a built in jQuery function called $.fadeToggle():

function toggleTestElement() {
    $('#testElement').fadeToggle('fast');
}

There's no need, just use fadeToggle() on the element:

$('#testElement').fadeToggle('fast');

Here's a demo.